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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 37570.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37570.r1 | 37570o1 | \([1, 1, 1, -88440, 5767865]\) | \(3169397364769/1231093760\) | \(29715610577469440\) | \([2]\) | \(294912\) | \(1.8597\) | \(\Gamma_0(N)\)-optimal |
37570.r2 | 37570o2 | \([1, 1, 1, 281480, 41872057]\) | \(102181603702751/90336313600\) | \(-2180499002725638400\) | \([2]\) | \(589824\) | \(2.2063\) |
Rank
sage: E.rank()
The elliptic curves in class 37570.r have rank \(1\).
Complex multiplication
The elliptic curves in class 37570.r do not have complex multiplication.Modular form 37570.2.a.r
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.